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Hartmann Testing The Telescope
Hartmann testing the telescope can be carried out by placing a Hartmann mask (a screen with holes in it) at the exit pupil of the telescope where the moving baffle and pupil baffles are to go. Out of focus images of stars are obtained with sufficiently long exposure times to average out seeing. Images of the spots are obtained and the centroids of the spots measured and compared with the spot positions in an ideal telescope. The residuals are then analysed and yield a measurement of the aberrations of the telescope.
Note that as the aberrations are field dependent, measurements at different positions in the field are required, and are expected to yield different spot patterns as a function of position in the field. The need to make measurements over the entire field of view requires that the testing be carried out with a camera that can see the entire field of view (such as SALTICAM).
The resulting spot patterns can then be compared with those expected from misaligning M4 or M5 (or any other optic in the telescope). As an example of the aberrations that might be expected, calculations have been carried out and are shown in: Sensitivity Analysis Of The SAC.

Fig. 1: 90-hole Hartmann mask schematic

Fig. 2: Example of full SALTICAM Hartmann image (left) and zoomed version of part of it (right)
Observational Data
The observational implementation of the Hartmann testing scheme was carried out as follows:
  • A 90 hole Hartmann mask (illustrated in Fig. 1 above) was placed at the exit pupil of the telescope.
  • The telescope was defocused by 3 mm of tracker movement. Because of the mask, out-of-focus stars then look like patterns of spots (see the example image shown above in Fig. 2 along with a zoomed-in view at right). The images were captured by SALTICAM (whose internal focus was shifted by -1 mm to compensate for the aberrations introduced by using it with SALT so far from focus).
  • Exposure times of 30 to 90 sec were used to ensure that atmospheric seeing was averaged out. Moderately sparse fields were chosen to avoid overlapping spot patterns, but denser sampling of the field of view was achieved by taking an image, then moving the telescope 60 arcsec, taking another image, and repeating a few times. The collection of images obtained in this way then constituted a "data set".
  • The sequence of exposures was arranged to begin just before the tracker passed through x=0 and y=0 (i.e. pupil centered on the primary mirror), and did not continue much beyond. The intention here is to obtain all images with the telescope entrance pupil as close as possible to being centered on the primary mirror.
  • Each image was then debiased and demosaiced and a CCD photometry program was used to determine the centroids of the spots in each "Hartmann patch" corresponding to a specific star: for example, the zoomed -in image shown in Fig. 2 (right) has 3 usable Hartmann patches corresponding to 3 stars - two at upper left and a fainter one at upper right - with about 65 spots in each patch.
A single data set is illustrated in Fig. 4 below. Note that some of the patches are overlapping in the illustration. This is not a problem as they were obtained from different images within the data set (with a move of the telescope in between as described above), and are labelled and analysed separately.

Fig. 4: Example data set comprised of 4 individual Hartmann images
Models
It was not possible to move SALTICAM or arrange re-imaging optics in front of it to sample two different place along the optical axis, thereby yielding two Hartmann images as used in the classical Hartmann technique. Likewise, shifting the telescope focus would change the optical configuration under test and is undesirable. So the observed spot positions were compared to "modeled" ones, generated by the optical ray tracing program Zemax, using the "as designed" prescription for the telescope and SALTICAM, but amended by the insertion of the Hartmann mask at the exit pupil and placing the telescope 3 mm out of focus. The model spot centroids were generated by using Zemax to trace rays from point sources at infinity distributed all over the science field of view. Centroids were determined from the intersections of the rays from a given point source (star) with the focal plane. We will refer to the set of centroids generate from this procedure as originating from the "perfect telescope". The perfect telescope set of spot patches are shown in Fig. 5 below; the plot is in pixel co-ordinates on the SALTICAM CCD.

Fig. 5: "Perfect Telescope" model Hartmann spot patches
We believe that this procedure is valid as the positions of the holes in the Hartmann mask (the most critical aspect) was set by the accuracy of the CNC milling machine which made the mask and this is expected to be accurate to about 10 microns. Nothing in the subsequent analysis gave us to believe that using model centroids for comparison with the observed ones was incorrect or inappropriate.
Analysis
An analysis program was written to read in the observed data and perfect telescope model and do a comparison analysis. The superposition of the observed data set (Fig. 4) and the perfect telescope model (Fig. 5), is shown in Fig. 6 below (blue being the model and black being the observational data).

Fig. 6: Superposition of observed and model spot patches
The first step in the analysis is to identify a model patch with each observed one. This was done on the basis of "nearest neighbour" (see Fig. 6). The model patch pixel co ordinates are then linearly shifted until the best match is achieved. The result of the procedure is illustrated in Fig. 7.

Fig. 7: Matching of the model spot patches to the observed patches
The next step is to match the individual spots within a patch. This is again done on the basis of "nearest neighbour" and is illustrated in Fig. 8 for 4 example patches from more than 50 in the observed data set described above.

Fig. 8: Matching of individual spots for 4 representative patches
Again, the model spots are coloured blue and the observed data are coloured black. The connecting lines show which observed spots are identified with which model spots (to enable a check for obvous misidentifications).
It is clear from Fig. 8 that the observed Hartmann spots do not match those from the model of the perfect telescope; this is to be expected of course (otherwise there would be no image quality problem!). The deviations of the observed spots from the perfect telescope spots are not random: their size and orientation show systematic behaviour as a function of position within the pupil, as well as position within the science field of view.
Misalignment Models
The next step is to determine a model spot pattern which does match the observed pattern. To do this, the same Zemax software used to generate the perfect telescope spot centroids was employed, but this time with a slightly different optical prescription: one of the elements (SAC mirrors M4 or M5 or M3), or the M4+M5 combination, or the whole SAC, was decentred or tip/tilted, and the spot centroids were calculated as before. In this case, however, the centroids of the perfect telescope were subtracted so that the output was a differential with respect to the perfect telescope. Individual sets of differentials were calculated for the x and y directions for decentres, and for tip/tilts, for all the optical elements and combinations mentioned above. Altogether, over 20 such sets of differentials were computed, as laid out in the Table below. A few models were computed for M4 with astigmatism and coma applied to the figure of the mirror - interferograms were delivered with this mirror showing no such misfiguring; these models were included just to illustrate the effect of these optical imperfections.
Full
SAC / M4 / M5 / M4+
M5 / M3
x tilt 0.01 deg / x tilt 0.1 deg / x tilt 0.07 deg / x tilt 0.4 deg / x tilt 0.1 deg
y tilt 0.01 deg / y tilt 0.1 deg / y tilt 0.07 deg / y tilt 0.4 deg / y tilt 0.1 deg
x decent 0.5 mm / x decent 0.5 mm / x decent 1.0 mm / x decent 0.15 mm
y decent 0.5 mm / y decent 0.5 mm / y decent 1.0 mm / y decent 0.15 mm
x astig
y astig
x coma
y coma
The aim is to obtain a match to the observed Hartmann spot patterns using the perfect telescope spot pattern, but with the individual spots shifted by a linear combination of the differentials calculated in the manner just described. If such a combination can be shown to 'fit', that would then suggest strongly that the image quality problems of SALT can be explained by the fitted model, and indicate the way forward in remedying the problem.
The fitting software was tried out by generating a set of "observed" spot patterns using the misalignment models: the synthetic data comprised 0.5 mm of decentre of M4 in both x and y, as well as compensating tip/tilt of the tracker of 0.01 degree in x and y. The resulting spot pattern is shown in Fig. 9 below. Notice how, compared to the perfect telescope patterns (Fig. 5), the spots in the lower part of each patch are "bunched up", and those at the top of the patches are "expanded".

Fig. 9: Synthetic data used to test the model fitting software
The results from the software reflected what had been used to construct the synthetic data, thereby giving confidence in the correct functioning of the software.
Results
The first attempt to fit the real observational data considered the data set described above (comprising fits files S200604260006-9.fits), obtained on 26 April 2006. Any difference in sizes of the Hartmann patches is the result of a difference in focus across the field. This focus difference is evident from the top two panels of Fig. 8. The top panel shows a Hartmann patch arising from the lower right of the field of view (see the inset in the panel which indicates where the patch occurs in the field of view). The second panel occurs near the top left of the field of view. In the top panel, it is evident that the black dots (observed spot centroids) fall systematically outside their corresponding blue (perfect telescope) counterparts. On the other hand, in the second panel, the reverse is true. There is thus a focus gradient over the field (as we observe with real stars). This focus gradient is most obvious in Fig. 10 which shows the scale factors by which the radius of the observed patches differs from the perfect telescope patches (all of which have the same focus and therefore the same size). it is clear that there is a focus gradient running from top left to bottom right, as expected.

Fig. 10: Scale factors by which the average radius of the observed patches differs from the corresponding perfect telescope patches.
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© SAAO 2006